ROTHESAY ACADEMY

MATHEMATICS DEPARTMENT

FIRST LEVEL THIRD LEVEL

QUADRILATERALSPATHWAY 1 BLOCK 4

SQUARE, RECTANGLE AND PARALLELOGRAM

Learning Intention

Identify the key properties of a Parallelogram

Success Criteria

Understand angular properties of a Parallelogram

Show all the correct working

Four equal sides

Four equal angles (all 90o)

Angles add up to 360o

Diagonals bisect at 90o

𝐴 = 𝑙 × 𝑙

SQUARE

𝑙

𝑙

Two pairs of equal sides

Four equal angles (all 90o)

Angles add up to 360o

Diagonals bisect but not at 90o

𝐴 = 𝑙 × 𝑏

RECTANGLE

𝑙

𝑏

Two pair of equal sides

Two pairs of equal angles

Angles add up to 360o

Diagonals bisect but not at 90o

𝐴 = 𝑏 × ℎ

PARALLELOGRAM

ℎ

𝑏

PARALLELOGRAM

Calculate the size of the missing angles

Angles in a triangle

add to 180

180 – (72 + 80) = 28o

28o

Z Angle = 28o

28o

Z Angle = 80o

80o

Angles in a triangle

add to 180

180 – (28 + 80) = 72o

72o

NOW YOUR TURN

TeeJay Level E

Page 210 Exercise 2

Q10 – Q13

Page 221 Exercise 6

Q9 – Q11

RHOMBUS

Learning Intention

Identify the key properties of a Rhombus

Success Criteria

Understand angular properties of a Rhombus

Show all the correct working

Four equal sides

Two pairs of equal angles

Angles add up to 360o

Diagonals bisect at 90o

𝐴 = 𝑑1 × 𝑑2 ÷ 2

RHOMBUS

𝑑1

𝑑2

RHOMBUS

Calculate the size of the missing angles

Symmetry = 26o

26o 26o

26o

Angles in a triangle

add to 180

180 – (26 + 90) = 64o

64o

Symmetry = 64o

64o

64o 64o

NOW YOUR TURN

TeeJay Level E

Page 213 Exercise 4

Q4, Q9 – Q15

KITE

Learning Intention

Identify the key properties of a Kite

Success Criteria

Understand angular properties of a Kite

Show all the correct working

Two pairs of equal sides

One pair of equal angles

Angles add up to 360o

Diagonals meet at 90o

𝐴 = 𝑑1 × 𝑑2 ÷ 2

KITE

𝑑1

𝑑2

Two pairs of equal sides

One pair of equal angles

Angles add up to 360o

Diagonals don’t meet

𝐴 = 𝑑1 × 𝑑2 ÷ 2

V-KITE

𝑑1

𝑑2

KITE

Calculate the size of the missing angles

Symmetry

65o

Angles in a triangle

add to 180

180 – (65 + 90) = 25o

25o

Angles in a triangle

add to 180

180 – (20 + 90) = 70o70o

25o

70o

20o

NOW YOUR TURN

TeeJay Level E

Page 218 Exercise 5

Q5, Q7, Q9 – Q11

TRAPEZIUM

Learning Intention

Identify the key properties of a Trapezium

Success Criteria

Understand angular properties of a Trapezium

Show all the correct working

One pair of parallel sides

Not usually any equal angles

Angles add up to 360o

Diagonals don’t bisect

𝐴 = ℎ(𝑎 + 𝑏) ÷ 2

TRAPEZIUM

ℎ

𝑎

𝑏

TRAPEZIUM

Calculate the size of the missing angles

Angles add to 180

180 – 71 = 109o

109o

Angles add to 180

180 – 125 = 55o

55o

NOW YOUR TURN

TeeJay Level E

Page 224 Exercise 7

Q2 – Q7

Square Four equal sidesFour equal

angles

Angles add up

to 360o

Diagonals

bisect at 90o 𝐴 = 𝑙 × 𝑙

RectangleTwo pairs of

equal sides

Four equal

angles

Angles add up

to 360o

Diagonals

bisect but not

at 90o

𝐴 = 𝑙 × 𝑏

ParallelogramTwo pairs of

equal sides

Two pairs of

equal angles

Angles add up

to 360o

Diagonals

bisect but not

at 90o

𝐴 = 𝑏 × ℎ

Rhombus Four equal sidesTwo pairs of

equal angles

Angles add up

to 360o

Diagonals

bisect at 90o 𝐴 = 𝑑1 × 𝑑2 ÷ 2

KiteTwo pairs of

equal sides

One pair of

equal angles

Angles add up

to 360o

Diagonals

meet at 90o 𝐴 = 𝑑1 × 𝑑2 ÷ 2

V-KiteTwo pairs of

equal sides

One pair of

equal angles

Angles add up

to 360o

Diagonals

don’t meet𝐴 = 𝑑1 × 𝑑2 ÷ 2

TrapeziumOne pair of

parallel sides

Not usually any

equal angles

Angles add up

to 360o

Diagonals

don’t bisect𝐴 = ℎ(𝑎 + 𝑏) ÷ 2

QUADRILATERALS SUMMARY